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JP0450105 the SMORES Capability for Minimum Critical Mass

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JP0450105 the SMORES Capability for Minimum Critical Mass JAERI-Conf 2003-019 JP0450105 The SMORES Capability for Minimum Critical Mass Determination Y. KARNf, D. REGEV, E. GREENSPAN' I,S. GOLUOGLL, L.M. PETRIE'and C.M HOPPER' Uni"rsity of California,Berkeley, California94720-1730, USA 2Oak Ridge National Laboratory,P. 0. Box 2008, Oak Ridge, Tennessee 3 7831-6370, USA The purpose of the present work is to illustrate the capability of SMORES - a nw sequence incorporated in SCALE-5, for automated minimurn critical mass (MCM) determination. The illustration Ls de by identilytrig the MCM of spherical systems of "U, U or "Pu moderated and reflected with either D20 or a combination of polyethylene and Be. he latta povide the lowest critical mm of, respectively, 151.7 g, 202.2 g and 119.0 g. These masses are close to a factor of 2 lower than the MCM of the corresponding fissile material with D20 and close to a factor of 4 for the MCM H20. The fissile material concentration exhibit a spike rim the core outer boundary at the interface between the poyethylene a Be. The SMORES sequence of SCALE could be useful fbr determining margins of subcriticality and for oer applications encountered by tic criticality safety cmmunity. KEYWORDS: SMORES; SCALE, Minimum CriticalMass; Maximum ke 233 U; 235 U; 239p" 1. Introduction search for the minimum crfical mass or for the minimum mass that can provide a pecified k < .0. A new prototypic analysis sequence, SMORES The ppose of the pesent work is to illustrate the (Scale Material Optimizanori and REplacement capability of the new SCALE sequence fb mmum Sequence), was - recently developed for critical mass MCM) determination. incorpoation into the SCALE-5 code package'). The illustration is done by appyirig the SMORES SMORES, provides for a semi-automatic search for sequence to determine the MCM of two types of either the maximinn kff of a given amount of systems: (A) A system consisting of a single fissile specified fissfle material, or the mmum critical material moderated and reflected by heavy-water and mass. It is described in detail in reference 2 and also M A system consisting of a singje fissile material in references 3 4 and 5. combination with two moderating materials - Very briefly, the search procedure proceeds as poyethylene (Poly) and berylliurn (Be). fbllows: Befbre starting the optimization process, a Type A systems were found by previous researchers rekrence system is defined This oxides the core to offer the lowest MW of a given fissile material radio or thickness and cposition and reflector when in combination with a sgle rnoderating/reflecting thickness and composition. Using firA order material. 7-9) T B systems were considered in a perturbation theory Equal Volurne Replacement previous tu;r)bt considered only 29pU fissk isotope Reactivity Worth (EVRRW) traverses are calculated and used infinit dution au&sections. for a system consdacm the com on of wch The following illustrations pertain to problems is a design variable. An EVRRW of material i with characterized by a sle fel aterial. Recently, the respect to refmnce material I is the reactivity effect SMORES capability has been expanded4) to enable search of rlacing a cubic centimetm of matenal I by the fbr maximum kr for Pstems with any number of fuel same volume of material For minimurn critical and non-fuel constituents. he ew capability Ls riot mm problems the EVRRW guide an automated incorporated, yet, within SCALE. redistribution of the systern conskmts so as to many= the fjel inventory while keeping k at or 2. Mustrations very close to .0. The optimization process is iterative, it proceeds until the EVRRW distribution 2.1 MCM in D20 of the fuel becomes flat Mass the core and is lower The systems considered are 240 cm i rius spherm outside of the core. of D20 with several hundred gms of a fissile material. SMORES can be used to determine margins of The fissile material is initially unilbrmly distributed submticality by identilying the maximum value of over a central sphere that is 60 cm in drus. The sphere the effective multiplication factor, km that can is divk1ed into 120 half-centimeter-thick zones he result from a given mass of a given fissile aterial composition aoss a zone is constant The optimization when combination with specified moderating ad variable is the concentration of the fissile material reflecting materials. The identification of kmdr is each of the zones. accomplished sernimautornatically, using the Figure I illustrates the opfirrial ontration of J optimization strategy of the SWAN Code4fi). in practically finft D medium. The MCM is found Alternatively, SMORES can perform an automated to be 344.84 g 2 U. Te uranium occupies the CorrespondingauthorTel. 001-510-643-9983,Fax. +001-510-643-9685,E-niail: gehudnuc.berkeley.edu 55 - JAE RI - Conf 2003-019 innermost 32 cm spherical region, and its 4.OE-0-4 - concentration monotonously increases towards the center. Figure 2 shows the EVRRW distribution two successive iterations contending to the 23.OE-04 - optimal systern composition It is seen that do effectiveness fiinctiori Ls practimfly flat across the U. zones that contain 131U and is lower in a o OE2.OE-04 zones This distribution unplies that the arrived at .20 compositiori Ls the optimal; no shuffling of constituents can finther increasekr 1.OE-04 C%1 4.OE-04 O.OE+00 0 10 20 30 40 50 60 c 2 3.OE-04 Radius (cm) U. Optimal 3 diStnbUfion in D yielding 11 Fig. 3 minimurn critical mass of 295.60 g. R 4.DE-04 I.OE-04 ....... 0 3.OE-04 O.OE+00 0 10 20 30 40 50 60 U. Radius (cm) 0 E2.OE-04 Mg I Optima 1211U dis:iribution in O yielding minimum critical ass of 344.84 g. 1.OE-04 Of 0.022 - O.OE+00 f......... ...... ........ 0.018, 0 10 20 30 40 50 60 Radius (cm) 0.014 - 0.010 Fig. 4 Optimal 139pU distribution in D yielding minimum critical mass of2O4.24 g. 0.006 .... .... 1 0 10 20 30 40 50 60 4.OE-04 - Radius (cm) c .2 'U 3.OE-04 - Fig. 2 Equal Volume RepLacement Reactivity LL Worth traverses in successive iterations 'El 2.OE-04 - cotirsponding t the optimal composition of Fig. 1. .2 0 A similar analysis done for otha fissile materials IL 1.OE-04 for 2 g for 239pU resulted in 295.60 J, 204.24 and 135.96 g for 41pLL Te geral shape of the fissile rnaterial distribution Ls similar t that of O.OE+00 Figure I but the core radius and the peak 0 10 20 30 40 50 60 concentration are fissile nuiterial dependent Fgure Radius (cm) 3 shows the optimal composition of 233U in DD while Figure 4 shows the optimal 239 Pu-1320 system Optimal 241pU distribution and Figure shows the optimal 241Pu-D20 system. Fi.g.5 in D20 yielding minimum critical mass of 135.96 g. - 552 - JAERI-Conf 2003-019 The esults for the 239pU - DP system can be Figur 9 shows the effect of zone thickness on the compared with results orted by Yatdl. The optimal 2 &tnbUfiorL The mum Critical mass minimum critical mass at roorn temperature was value s practically the same for both zone ducknesses faind8 t be 390 g; it corrosponds to a thin shell of considered. Figures IO and I I show the corresponding 2N Pu flat Ls 50 cm in outer diameter and is polyethelene and berythurn optimal ffistribution. immersed in a 240 cm cube of D20. Heavy water Whereas the optimization using 0. c thick zones fiflS the 9pir Sphere interior a WeU. results in a complete separation between the two From the close to a factor of two difference in moderators, the optimization using the 025 cm zones the critical mass it appears that the optimal spatial results in a sght mixing of the two. diStribirtion of 29pU identified by SMORES is significantly more reactive than that of the spherical 6.OE-03 Al shell of eference S. In or to verify this hypothesis the SCALE sequence used for the 5.OE-03 - SMORES analysis was applied for calculating ker .2 of 240 cm in dius helical systems comprising of 4.01E-03 a sgle 204.24 g of shell with inside and U. outside the shelL Te maximum kr was found to r- 3.OE-03 - be 0883 - lower thari for the SMORES defined .0 core kf = 1.0). It corresponds to a shell that is 50 > 2.OE-03 - cm in outer diameter. Poly Be In order to verify the SMORES minimurn critical C4 1.0E-03 mass calculations reported above MCNP was applied to calculate k for the system compositions O.OE+00 reported in Figures I through 5. The MCNP 0.0 5.0 10.0 15.0 20.0 calcuhded kff is very close to unity for a fbur Radius (cm) systems, as can be seen from Table . Table I Comparison of MCNP Versus SMORES Fig. 6 Optimal 2sU distribution with polyethylene and Calculated kE Values for MCM in D20 berylhum. moderaturs/reflectors yielding minimum critical mass of 201.22 g. Fissile SMORES MCNPkr material ka 6.OE-03 A - - -BT- 0.999999 0.99722±0.00092 = U 1.000000 0.99871±0.00085 1.000013 0.99765±0.00089 5.OE-03 .2 PU 1.000048 1.00014±0.00096 4.OE-03 - U. 2.2 MCM In Polyethylene and Beryllium r 3.01E-03 - Figure 6 shows the optimal position of a 20 , - Poly Be Type spherical system composed of 23J, Poly > m 2.OE-03 and Be.
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